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The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in applied mathematics and in the natural sciences (such as physics , biology , earth science , chemistry ) and engineering disciplines (such as computer science , electrical engineering ), as well as in non-physical systems such as the ...
Modeling and simulation (M&S) is the use of models (e.g., physical, mathematical, behavioral, or logical representation of a system, entity, phenomenon, or process) as a basis for simulations to develop data utilized for managerial or technical decision making. [1] [2]
The implementation of a multiphysics simulation follows a typical series of steps: [1] Identify the aspects of the system to be simulated, including physical processes, starting conditions, and the coupling or boundary conditions among these processes. Create a discrete mathematical model of the system. Numerically solve the model.
The second step is discretization, where the weak form is discretized in a finite-dimensional space. After this second step, we have concrete formulae for a large but finite-dimensional linear problem whose solution will approximately solve the original BVP. This finite-dimensional problem is then implemented on a computer.
By a model is meant a mathematical construct which, with the addition of certain verbal interpretations, describes observed phenomena. The justification of such a mathematical construct is solely and precisely that it is expected to work—that is, correctly to describe phenomena from a reasonably wide area.
Steps in numerical modeling. The first step in numerical modeling is to capture the actual geological scenario quantitatively. For example, in mantle convection modeling, heat equations are used to describe the heat energy circulating in the system while Navier–Stokes equations describe the flow of viscous fluid (the mantle rock).
Models use basic assumptions or collected statistics along with mathematics to find parameters for various infectious diseases and use those parameters to calculate the effects of different interventions, like mass vaccination programs. The modelling can help decide which intervention(s) to avoid and which to trial, or can predict future growth ...
The field of system identification uses statistical methods to build mathematical models of dynamical systems from measured data. [1] System identification also includes the optimal design of experiments for efficiently generating informative data for fitting such models as well as model reduction.